Problem: Daniel is 4 times as old as Umaima. Six years ago, Daniel was 6 times as old as Umaima. How old is Daniel now?
Explanation: We can use the given information to write down two equations that describe the ages of Daniel and Umaima. Let Daniel's current age be $d$ and Umaima's current age be $u$ The information in the first sentence can be expressed in the following equation: $d = 4u$ Six years ago, Daniel was $d - 6$ years old, and Umaima was $u - 6$ years old. The information in the second sentence can be expressed in the following equation: $d - 6 = 6(u - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to solve our first equation for $u$ and substitute it into our second equation. Solving our first equation for $u$ , we get: $u = d / 4$ . Substituting this into our second equation, we get: $d - 6 = 6($ $(d / 4)$ $- 6)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $d - 6 = \dfrac{3}{2} d - 36$ Solving for $d$ , we get: $\dfrac{1}{2} d = 30$ $d = 2 \cdot 30 = 60$.